how to change the design of the header?
It really depends on what you want to change. You can write your custom CSS and add it inside WordPress dashboard - Appearance - Theme Options - Other.
There are also several color pickers available via Theme Options - Header. This will help you to change colors for all aspect of theme menu. Other things like size, fonts and other should be changed via writing your own Custom CSS.
Can I change the fonts and colors in the css file menu theme?
Feel free to write your own CSS on top of existing one. The best way is to add your CSS inside Theme Options - Other - Custom CSS field or inside Custom CSS generated by plugins such as Jetpak has one.